"One-Arm" was the moniker attributed to the wampa of female gender that Luke Skywalker encountered within the icy cave located on Hoth during the year 3 ABY.
On her native world of Hoth, a female wampa dwelled within the ice cave into which Luke Skywalker was dragged after a male wampa assaulted him while he was riding a tauntaun. Upon regaining consciousness, Skywalker found himself suspended from the cave's ceiling. As he attempted to understand his situation, Luke observed the wampa consuming the remains of a tauntaun. Using the Force, Luke summoned his lightsaber from the ice, freed himself, and escaped with facial injuries and contusions. During this escape, Skywalker defended himself with his lightsaber, resulting in the wampa losing one of its arms.
Later, this wampa became the leader of a group of other wampas, organizing them into a force capable of attacking the hunters who arrived on Hoth. They even figured out how to infiltrate Echo Base stealthily. In 12 ABY, when Skywalker returned to Hoth alongside Callista Ming, the wampa recognized him and attempted to kill him once more. Luke killed the wampa in the ensuing battle.
Ultimately, the wampa became known by the name "One-Arm."
In Star Wars: Episode V The Empire Strikes Back, when One-Arm's arm is severed, the detached limb appears to be noticeably shorter than what would be required to account for the full length of the arm she is shown to be missing in the subsequent shot.